Cyano-Polycyclic Aromatic Hydrocarbon Interstellar Candidates: Laboratory Identification, Equilibrium Structure and Astronomical Search of Cyanobiphenylene

The interplay between laboratory rotational spectroscopy and radio astronomical observations provides the most effective procedure for identifying molecules in the interstellar medium (ISM). Following the recent interstellar detections of several Polycyclic Aromatic Hydrocarbons (PAHs) and cyano derivatives in the dense molecular cloud TMC-1, it is reasonable to consider searching for other cyano-PAHs in this astronomical source. We present a rotational spectroscopy investigation of the two cyano derivatives of the PAH biphenylene, a plausible reaction product of interstellar benzyne. The rotational spectrum provided molecular parameters for the parent species and 14 monosubstituted isotopologues for each isomer. An accurate equilibrium structure was determined for both isomers using Watson’s mass-dependence method (rm(2)), offering information on its uncommon ring union. Astronomical searches for the cyanobiphenylene isomers have been undertaken in TMC-1, using the QUIJOTE line survey. No lines of any isomer were found in this astronomical source, but the experimental data will serve to enable future searches for these species in the ISM.


Synthesis of 2-bromobiphenylene (2-BBP).
To a stirred solution of biphenylene (BP, 200 mg, 1.31 mmol) in dry DMF (3.3 mL), neat NBS (257.3 mg, 1.44 mmol) was added.The solution was stirred overnight a room temperature and then transferred to a flask with ice-cold water.The precipitate was filtered and washed with a large amount of water to remove the residual DMF.The compound was taken up with EtOAc, concentrated under reduce pressure and filtered through a short plug of silica gel (hexane) to afford 2-bromobiphenylene (2-BBP) as a yellow oil (300 mg, 99%).Analytical data were in accordance with literature.

Structural Methods
The determination of the equilibrium structures (re) of 1-cyano and 2-cyanobiphenylene was conducted independently using structurally corrected ab initio calculations and the Watson's mass-dependent method 2 (rm (2) ).

Structurally-corrected ab initio estimation of the equilibrium structure
The first estimation of the equilibrium structure used second-order Moller-Plesset 3 perturbation theory (MP2) and a correlation-consistent triple-ζ basis set from Dunning (cc-pVTZ 4 ).These calculations are shown in Tables S1 and S2.The MP2/cc-pVTZ level of theory is able to predict the bond angles with an accuracy better than 0.3-0.4° in most cases. 5The ab initio structures then serve as starting point for the calculation of predicates which will later be used in the massaveraged structure of section 2 below.
For the carbon-hydrogen (CH) bond lengths, the MP2/cc-pVTZ method typically delivers values with accuracies better than 0.001 Å (see also Tables S1-S2). 6,7e case of the carbon-carbon (CC) bond is more complicated because the range of its length is large in the title compounds.Furthermore, the differences re(CC) -r(MP2/cc-pVTZ) are not constant because of the differences in hybridization of the carbon orbitals participating in the molecular bonds. 6,7However, a plot of this difference as a function of re shows that the difference varies almost linearly. 6,7From the ab initio calculations, it appears that the CC bond lengths in cyanobiphenylene are intermediate between double bonds and single bonds.For this category of partial double bonds, the equilibrium value is often longer than the MP2/cc-pVTZ value (see Table S3).A linear regression of the values of 40 molecules in Figure S2 gives the following result: with a correlation coefficient of 0.9982 and a standard deviation of the fit of 0.0017 Å.The sample of reference data is given in Table S3.There is however, an important exception: the CC bond lengths in a phenyl ring where the equilibrium value is shorter than the MP2/cc-pVTZ value. 8In this case, a linear regression of sixteen equilibrium distances (Table 1 of reference 8) gives: with a correlation coefficient of 0.9999999 and a standard deviation of the fit of 0.00055 Å.
This correlation has been found valid for bond lengths in aromatic molecules, but as cyanobiphenylene is antiaromatic, it is not obvious that it can be used.There are at least two ways to make sure that it can be applied in our case: i) A comparison of results with the rs values when they are believed to be accurate, see Tables S1-S2 (final structures).In particular, for the bond length C4b-C5, equation (S2) gives 1.372 Å whereas the rs value is 1.372(1) Å.
ii) A more stringent confirmation will be given by the rm-fit of the next section which may be used to examine the compatibility of the predicates (i.e. the corrected MP2/cc-pVTZ values) with the rotational constants.For the CC ring bonds, it will be shown that, when there is a large discrepancy, the fitted value is smaller than the predicate value.
This procedure confirms that it is better to use Eq.(S2) for the CC ring bonds.
Concerning the carbon-carbon bridge (C4a-C4b) bond length, the situation is easier because, although it is between two multiple bonds, it behaves as a single bond.An Atoms-in-Molecules (AIM) calculation for 1-cyanobiphenylene indicates that the ellipticity 9 for this bond is only 0.037 whereas it is 0.215 for C2C3 and 0.150 for C4aC8b, see Tables S4-S5.For 2cyanobiphenylene, the ellipticity is 0.038.As shown in Table S1, for such a long bond, the MP2/cc-pVTZ value of 1.5072 Å for 1-cyanobiphenylene is close to the equilibrium values.
Finally, for the carbon-nitrogen (CN) triple-bond length the situation is still easier because the variation range of the equilibrium distances is small.Therefore, it may be assumed that the correction is constant.A selection of equilibrium values for CN bonds is shown in Table S6.
The accuracy of the structural calculations can be checked qualitatively by comparison with the substitution structure 10 method (rs), provided that a selection of atoms is chosen with large cartesian coordinates.The substitution structures are included in Tables S1-S2.The uncertainties in the substitution structure calculations have been discussed elsewhere. 11A satisfactory comparison of some bond length predicates with the substitution structure is shown in Table S7.

Mass-dependent method
The mass-dependent structural method of Watson et al. 2 (rm) permits obtaining a very accurate equilibrium structure for small molecules from the zero-point moments of inertia of a set of isotopologues.Unfortunately, the Watson method has considerable requirements and often fails for large molecules.This is mainly due to the fact that the number of structural parameters to fit can be very large, requiring a considerable number of isotopic species.Therefore, the system of normal equations of the least-squares fit may be ill-conditioned.However, an easy way to remedy this difficulty is to use the method of mixed regression, 12 where the rotational constants are supplemented by structural parameters from ab initio calculations, here from the initial MP2/cc-pVTZ structurally corrected predictions of section 1.
The rm method was already employed with success for several moderately large molecules like ethynylcyclohexane (C8H6), 13 diallyl disulfide (C6H10S2), 14 diphenyl disulfide (C12H10S2), 8 or fructose (C6H12O6). 15The determination of the Watson rm structure for the cyanobiphenylenes (C13H7N) represents a considerable advance because of the structural interest of the molecule, probably one of the largest for which this method was attempted.
The Watson method relates the ground-state and equilibrium moments of inertia by either explicit functions of degree ½ on the equilibrium moments of inertia (rm (1) method) or by a two-parameter model including an additional 1/(2N-2) power dependence on the reduced atomic masses (rm (2) method).In this way, the ground-state moment of inertia  0  for each inertial axis  can be approximated by In this equation,  is the number of atoms, mi their respective masses and   and   are the two fitting rovibrational parameters.
The rm (2) method has two advantages: i) It allows to obtain a reliable structure without too much computational work, as there is no need to calculate rovibrational corrections for all isotopologues (all the more so that it does not solve the problem of ill-conditioning) ii) It permits to check that the experimental rotational constants are compatible with the (corrected) ab initio structure.
The statistical diagnostics for the rm (2) fit use the Studentized residual to detect outliers and the diagonal elements of the Hat matrix which permit to detect leverage values (a leverage is high when a small change of the input value causes a large change in the solution). 16In the present case we used fifteen isotopologues for each isomer (45 moments of inertia), and fitted the molecular structure assuming only the planarity of the ring system and the nitrile group.
The fit results indicate that there is no outlier and that the weighting was adequate.
However, the condition number is high, κ = 1.1×10 5 .Therefore, some parameters may be less accurate than indicated by their standard deviation. 12The analysis of the variancedecomposition proportions shows that this problem does not affect the bond lengths but only a few bond angles.This is fortunate because, as shown below, it is relatively easy to confirm their accuracy.However, some rovibrational parameters are poorly determined, see Table S1.For this reason, it was assumed that the fitting parameters for the b and c axes are the same (cb = cc and db = dc).As shown in Table S1, these constraints do not affect the values of the parameters.
In the final fit, the internal coordinates of the hydrogen atoms where kept fixed at their MP2/cc-pVTZ values.This simplification may bias the parameters and affect their standard deviation.For this reason, the fit was repeated for 1-cyanobiphenylene freeing all the parameters and using the MP2/cc-pVTZ values as predicates for the coordinates of the hydrogen atoms.The new parameters from this global fit are almost identical to those of the reduced fit and their standard deviations are not increased, see Table 1.

Discussion
The quality of the final structures in Tables S1 and S2 is discussed below.A first check was made by calculating the rovibrational corrections for 2-cyanobiphenylene with the help of the ab initio MP2/cc-pVTZ anharmonic force field.The results (in MHz): ∆A = Ae -A0 = 17.033; ∆B = 1.708; ∆C = 1.533 are in reasonable agreement with the values deduced from the rm (2) fit: ∆A = 17.644; ∆B = 1.747; ∆C = 1.568.

Analysis of the bond angles
There are several ways to check the accuracy of the bond angles

Ab initio optimizations
The quality of the ab initio optimizations was discussed in section 1.

Effective (r0) structure
Contrary to the r0 bond lengths, the effective bond angles (∠0) are often a good approximation of the equilibrium values.An analysis of 45 angles gave a median absolute deviation (MAD) of 0.2° corresponding to a standard deviation of 0.3°. 17For 1cyanobiphenylene, the MAD is 0.25° corresponding to a standard deviation of 0.36°, the largest deviation, 1 °, being for the C7C8C8a bond angle.However, the r0 value, 116.1(18)°, is rather inaccurate.Furthermore, for this angle there is a good agreement between the  m (2) value and the MP2/cc-pVTZ value.Finally, the effective and  m (2) values of the ∠(C4C4aC8b) angle are also in good agreement.This a further indication that the  m (2) angles are accurate.For 2-cyanobiphenylene, the MAD is 0.4° corresponding to a standard deviation of 0.6°, the largest deviation being 0.7°, for the ∠(C4a-C8b-C1) angle, but this is smaller than the standard deviation of the ∠0 value, 0.8°.

Zero-point average structure (r α )
The ∠ α (or ∠z) angles are also a good approximation of the equilibrium values, the difference being generally smaller than 0.2°. 17Although the ∠ α angles of biphenylene are not precise, they are in good agreement with our results.In particular, the ∠ α (C4aC4bC5) value of biphenylene, 147.5 (6)° is in excellent agreement with the  m (2) value of 147.52(5)° of 1cyanobiphenylene.

Analysis of the bond lengths
The situation for the bond lengths is more complicated.First, the comparison with the rs structure does not help because some Cartesian coordinates of the atoms C4a and C8b are quite small (a[C4a] = 0.066 Å and b[C8b] = 0.041 Å).For this reason, the rs value of the bond length C4aC8b is inaccurate.
For the CC bonds, it is possible to calculate the electronic density at the bond critical point with the Atom in Molecules method. 9(see Figure S3 and Tables S4 and S5).This parameter, ρb, gives the amount of electron density shared between the two bonded atoms and is roughly proportional to the bond length.Indeed, a plot of the  m (2) CC bond lengths as a function of ρb in Figure S4 shows a good correlation (correlation coefficient, 0.995) for 1cynobiphenylene and, thus, confirms the reliability of the  m (2) structure.Figure S4 clearly shows three almost linear sections: first, three points corresponding to long CC bonds C8aC8b, C4aC4b, and C1Cα.For these bonds, ε ≤ 0.7.Then, bonds with 0.15 ≤ ε ≤ 0.16 whose length is between 1.411 Å and 1.417 Å.Finally, the third section 0.20 ≤ ε ≤ 0.22 whose length is between 1.371 Å and 1.393 Å.Another indication of the reliability of the  m (2) structure is that, as discussed above, all the bond angles are accurate.Figure S5 shows a similar representation for 2-cyanobiphenylene.

Upper limit of column density calculations
To compute upper limits to the column densities of 1-CNBP and 2-CNBP in TMC-1, we proceeded in this way.We first predict the line intensities under local thermodynamic equilibrium (LTE) conditions for the rotational temperature adopted and identify the lines that are predicted to be the most intense ones in the Q band.These correspond to the three lines shown in Figure 3.We then compute the 3σ upper limits to their velocity-integrated line intensity as: where rms is the noise level measured in the observed spectrum in the spectral region around each line (in antenna temperature scale and units of mK), δv is the spectral resolution of the spectrum in velocity (with units of km s -1 ), and ∆v is the full width at half maximum expected for the line (here taken as 0.60 km s -1 for TMC-1).We then calculate the column density that would be needed to account for the 3σ velocity-integrated intensity derived for each line in the previous stage, and adopt as 3σ upper limit to the column density the smallest value.
Table S1.Molecular structure of 1-cyanobiphenylene, including the ab initio calculations, the ab initio predicates, the mass-averaged equilibrium structure (rm (2) ), the effective structure (r0) and the substitution structure (rs).The final equilibrium structure corresponds to the rm (2) fit with four rovibrational parameters.In this fit all internal coordinates of the hydrogen atoms were fixed to the ab initio predicates.Alternative rm (2) fits are shown for comparison, using six rovibrational parameters (Fit 2) or the internal hydrogen atom coordinates (Fit 3).Table S2.Molecular structure of 2-cyanobiphenylene, including the ab initio calculations, the ab initio predicates, the mass-averaged equilibrium structure (rm (2) ), the effective structure (r0) and the substitution structure (rs).The final equilibrium structure corresponds to the rm (2) fit with four rovibrational parameters.All internal coordinates of the hydrogen atoms were fixed to the ab initio predicates.

Figure S3 .
Figure S3.Atoms-in-Molecules (AIM) representation for 1-cyanobiphenylene showing critical points at the C-C and C-N bonds of the molecule.See TablesS4 and S5for the electronic densities and ellipticities.

Figure S5 .
Figure S5.A representation of  m e. c b = c c and d b = d c .b All six rovibrational constants fitted.c All internal coordinates of the hydrogen atoms fitted.d Uncertainties expressed in parentheses in units of the last digit.
e. c b = c c and d b = d c .
a d Residual from the fit with Eq. (S1).

Table S6 .
Values for the C≡N equilibrium bond length (Å).References for the equilibrium structures, see page 15.
a S31

Table S7 .
A comparison of some of the ab initio predicates with the substitution structure calculation in TablesS1 and S2.